We have proposed two schemes to implement post-selected CPF and Toffoli gates in the coincidence basis by solely using linear optics. The comparisons between our proposed CPF gate and Toffoli gate and previous schemes are presented in Tab. REF  and Tab. REF , respectively. A maximally entangled photon pair [1]}, [2]}, [3]}, [4]}, [5]} (or two single photons [6]}, [7]}) is necessary for implementing a CNOT gate with the current existing maximum success probability of 1/4 (or 1/8).
Only one auxiliary single photon is introduced to accomplish our CPF gate with the success probability of 1/4. In addition, our approach to implement Toffoli gate is much more efficient than the synthesis one. Assisted by two independent single photons, our Toffoli gate is constructed with the current maximum success probability of 1/30. The presented two architectures provide an alternative insight into probabilistic quantum gates using linear optical elements and suggest that they maybe have various applications in photonic quantum information processing.
